Consolidated Statements of Shareholders' Equity - USD ($) shares in Thousands, $ in Thousands		Total	Common Stock Common Shares	Common Stock Class B Common Stock	Capital Surplus	Retained Earnings	Accumulated Other Comprehensive Loss
Balance at beginning of period at Aug. 28, 2021		$ 1,872,952	$ 1,524	$ 364	$ 89,257	$ 1,806,643	$ (24,836)
Balance at beginning of period (in shares) at Aug. 28, 2021			15,236	3,643
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income		103,404				103,404
Pension benefit liabilities, net	[1]	7,518					7,518
Change in fair value of derivatives	[1]	30					30
Foreign currency translation		(7,002)					(7,002)
Dividends declared		(21,658)				(21,658)
Shares converted			$ 1	$ (1)
Shares converted (in shares)			17	(17)
Share-based compensation, net	[2]	5,035			5,035
Share-based awards exercised, net	[1]	4	$ 4
Share-based awards exercised, net (in shares)	[1]		36
Repurchase of Common Stock		(44,412)	$ (21)	$ (4)	(1,161)	(43,226)
Repurchase of common stock (in shares)			(214)	(36)
Balance at end of period at Aug. 27, 2022		1,915,871	$ 1,508	$ 359	93,131	1,845,163	(24,290)
Balance at end of period (in shares) at Aug. 27, 2022			15,075	3,590
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income		103,674				103,674
Pension benefit liabilities, net	[1]	2,130					2,130
Change in fair value of derivatives	[1]	100					100
Foreign currency translation		(1,701)					(1,701)
Dividends declared		(22,288)				(22,288)
Share-based compensation, net	[2]	6,172			6,172
Share-based awards exercised, net	[1]	2	$ 2
Share-based awards exercised, net (in shares)	[1]		29
Balance at end of period at Aug. 26, 2023		2,003,960	$ 1,510	$ 359	99,303	1,926,549	(23,761)
Balance at end of period (in shares) at Aug. 26, 2023			15,104	3,590
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income		145,474				145,474
Pension benefit liabilities, net	[1]	(348)					(348)
Change in fair value of derivatives	[1]	(73)					(73)
Foreign currency translation		538					538
Dividends declared		(23,670)				(23,670)
Share-based compensation, net	[2]	6,534			6,534
Share-based awards exercised, net	[1]	4	$ 4
Share-based awards exercised, net (in shares)	[1]		36
Repurchase of Common Stock	[3]	(23,908)	$ (14)		(1,046)	(22,848)
Repurchase of common stock (in shares)	[3]		(140)
Balance at end of period at Aug. 31, 2024		$ 2,108,511	$ 1,500	$ 359	$ 104,791	$ 2,025,505	$ (23,644)
Balance at end of period (in shares) at Aug. 31, 2024			15,000	3,590

[1] These amounts are shown net of the effect of income taxes.

[2] These amounts are shown net of any shares withheld by the Company to satisfy certain tax withholding obligations in connection with the vesting of certain restricted stock units.

[3] These amounts are shown net of the effect of excise taxes.